A week after an artificially intelligent system invented a new method of multiplying number grids together, mathematicians come up with an even better way to do this task.
Two mathematicians have found a more efficient way to multiply rows and columns of numbers (matrices) together. They thus break the record of an artificial intelligence (AI) from the company DeepMind, which came up with a new method earlier this month.
From 98 to 95 steps
deep mind revealed on October 5 that his AI had achieved a breakthrough in matrix multiplication. This mathematical operation, where grids of numbers are multiplied together, is widely used in all kinds of software. The AI came up with a new way to multiply two 5-by-5 matrices in just 96 multiplications. That is 2 less than the previous record.
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Mathematicians Jakob Moosbauer and Manuel Kauers of the Johannes Kepler University in Austria were already working on their new approach to the problem. They make multiplication algorithms go through a process in which several steps in the algorithm are tested whether they can be combined.
Read in our previous news post how Deepmind’s AI made multiplication more efficient
‘We take an existing algorithm and apply a series of transformations that can lead to improvements in certain areas. Our technique works for every known algorithm. If we’re lucky, we’ll always need one multiplication less than before’, says Moosbauer.
After DeepMind made its breakthrough public, Moosbauer and Kauers used their approach to further improve the AI methodology. They succeeded: they managed to eliminate one more multiplication, so they can now multiply 5-by-5 matrices in just 95 steps.
New impulse
The duo shared the result in a preprint paper, an article that has not yet been peer-reviewed. ‘We wanted to publish immediately to be the first, because if we can find it in such a short time, there is a considerable risk that we will be outdone by someone else’, says Moosbauer.
The mathematicians’ paper focuses entirely on the multiplication of 5-by-5 matrices, but the method probably works for other sizes as well. Moosbauer and Kauers only share the result of their work in their article, and no details yet about the approach used. They promise to reveal it soon.
Moosbauer says the AI find has given new impetus to an area of mathematics that has long been underexposed. He hopes that other teams have now also started working with matrix multiplication algorithms.
More efficient software
Matrix multiplication is a mathematical operation that occurs in almost all software. Because it is used so much, a small improvement in the algorithms can quickly save a lot of computer time and energy.
DeepMind claims that its new algorithms increase the computational speed of computer components by 10 to 20 percent. This has been tested, among other things, with a graphics processor from computer manufacturer Nvidia and a tensor processing unit from Google. It is not clear whether such gains can also be made on ordinary devices that perform everyday tasks, such as smartphones and laptops.
Moosbauer is skeptical about this. Still, an improvement is worthwhile, because efficiency gains are also welcome for specific computer tasks, such as scientific simulations.
DeepMinds AI researcher Alhussein Fawzi said in a statement: ‘We hoped [ons werk] would elicit new ideas and approaches in the field of algorithmic discovery. It’s great to see others building on our work so quickly.’